Boundary Systems and Relative Motion

For example, consider a system that is moving in the x direction with a velocity Vs a fluid stream entering the system with a velocity in the x direction relative to the system of Vn, and a stream leaving the system with a velocity Vro relative to the system. The absolute stream velocity in the x 

Example 5-8 Turbine Blade. Consider a fluid stream impinging on a turbine blade that is moving with a velocity Vs. We would like to know what the velocity of the impinging stream should be in order to transfer the maximum amount of energy to the blade. The system is the fluid in contact with the blade, which is moving at velocity Vs. The impinging stream velocity is V, and the stream leaves the blade at velocity Va. Since V0 = Vro + Vs and V = Vri + Vs, the system velocity cancels out of the momentum equation  

If the friction loss is negligible, the energy balance (Bernoulli s equation) becomes 

Since the maximum energy is transferred when VD = 0, this reduces to 

That is, the maximum efficiency for energy transfer from the fluid to the blade occurs when the velocity of the impinging fluid is twice that of the moving blade. 

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